rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Elementary Functions
    sub title: Algorithms and Implementation
  name:
    name part: Muller, Jean-Michel.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2016
    edition: 3rd ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXV, 283 p. 40 illus. online resource.
  abstract: This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysi…
  table of contents: Introduction -- Introduction to Computer Arithmetic -- Part I: Algorithms Based on Polynomial Approximation and/or Table Lookup, Multiple-Precision Evaluation of Functions -- The Classical Theory of Polynomial or Rational Approximations -- Polynomial Approximations with Special Constraints -- Polynomial Evaluation -- Table-Based Methods -- Multiple-Precision Evaluation of Functions -- Part II: Shift-and-Add Algorithms -- Introduction to Shift-and-Add Algorithms -- The CORDIC Algorithm -- Some Other Shift-and-Add Algorithms -- Part III: Range Reduction, Final Rounding, and Exceptions -- Range Reduction -- Final Rounding -- Miscellaneous -- Examples of Implementation -- References -- Index.
  note: by Jean-Michel Muller.
  subject:
    topic: Mathematics
  subject:
    topic: Numerical analysis
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Algorithms
  subject:
    topic: Computer mathematics
  subject:
    topic: Mathematics
  subject:
    topic: Computational Science and Engineering
  subject:
    topic: Algorithms
  subject:
    topic: Numeric Computing
  subject:
    topic: Applications of Mathematics
  classification: QA71-90
  classification: 004
  related item:
    title info:
      title: Springer eBooks
  identifier: 9781489979834
  identifier: http://dx.doi.org/10.1007/978-1-4899-7983-4
  record info:
    record creation date: 161116
    record change date: 20161116173557.0
    record identifier: 978-1-4899-7983-4